1. Technical Field
This application is related to signal processing systems for compression, transmission, and reconstruction of a signal, and more particularly, to those systems suitable for use in microwave photonics applications.
2. Related Technology
High-speed digital signal processing and the development of microwave photonics systems are requiring faster and faster analog-to-digital conversion (ADC) hardware. The performance of ADC hardware continues to advance in support of these high-speed applications. For example, both wideband millimeter wave antenna systems and digital fiber optic communication links may require coverage out to 100 GHz and beyond in the future.
Digitization requirements have traditionally been based on the Shannon-Nyquist sampling theorem which states that a bandlimited signal, x(t), occupying a frequency range [0, fNy/2] Hz can be reconstructed at any point in time, provided that the waveform is known at a discrete set of equally spaced times no more than Δ=1/fNy seconds apart. Thus, to capture a 100 GHz signal, the time interval Δ between samples can be at most 1/200 GHz. Digitizers operating in the 200 GS/s regime are unlikely to be available in the near future.
Compressive sampling, which is also known as “CS”, “compressed sampling” or “compressed sensing”, was developed to estimate the values of the signal x when sampling at a lower rate. An important application of compressed sampling is the reconstruction of discrete samples of an analog signal at or above the Nyquist rate using a digitizer operating below the Nyquist rate.
Compressive sampling can be considered to be a set of nonadaptive signal processing techniques that address the ill-conditioned problem described in E. J. Candes, J. Romberg and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Info. Theory, 52(2), 489-509 (2006), E. J. Candes and T. Tao, “Near-optimal signal recovery from random projections: Universal encoding strategies?,” IEEE Trans. Info. Theory, 52(12), 5406-5425 (2006), and D. L. Donoho, “Compressed Sensing,” IEEE Trans. Inf. Theory 52(4), 1289-1306 (2006). Compressive sampling systems are described in R. G. Baraniuk, “Compressive Sensing,” IEEE Sig. Proc. Magazine, July 2007, 118-124 (2007).
J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg and R. G. Baraniuk, “Beyond Nyquist: Efficient sampling of sparse bandlimited signals,” IEEE Trans. Info. Theory, 56(1), 520-544 (2010) provides an overview of compressive sampling techniques.